Todays Schedule

1
Todays Schedule

• Reading Lathi 13.3 Carrier Systems
• Review
• Mini-Lecture 1
• Carrier Systems Coherent Detection
• Mini-Lecture 2
• Carrier Systems Incoherent Detection

2
Optimum Binary Receivers

• Symbols transmitted once every Tb seconds
• To transmit
• Send p(t) for a 1
• Send q(t) for a 0
• Noise is Gaussian

Decision 1 if r(Tb)gta 0 if r(Tb)lta
tTb
s(t)n(t)
r(t)
h(t) H(f)
Threshold Detector
r(Tb)
3
Carrier Systems
4
Minimizing PE
Q(b)

• Minimize probability of error

0.5
b

• Maximize beta to get small value for Q function

5
Results-White noise, threshold receiver, matched
filter

• Minimized PE is (For binary case PE Pb )
• Optimal threshold if P(0)P(1)

6
Applying the equations

• Bipolar signaling
• Polar signaling
• Orthogonal Signaling

7
Waterfall Curves

• Blue is bipolar, green-dashed is polar
• Bipolar has better performance by 3 dB at low Pb

8
Activity

• Which signaling scheme is better, bipolar or
  polar?
• Support your answer, quantitatively and
  qualitatively.
• Looking at slide 3, which signaling scheme does
  ASK map to? Which signaling scheme does BPSK map
  to?

9
Coherent Detection

• Detect pulse with r22Ep/N
• Matched filter then sample and detect
• Coherently demodulate, then filter out image with
  matched filter and sample/detect

10
Coherent Detection

• Must match phase of the input signal
• Since we are dealing with linear systems
• Input frequency band
• Mix down to baseband
• In the optimal case for white noise, with a
  matched filter and sampler(13.7a)

11
Binary Phase Shift Keying

• Phase of each signal is separated by pi
• Same as bipolar signaling

12
Amplitude Shift Keying

• Same as on/off (polar) signaling
• Requires 3 dB more power than BPSK in a coherent
  system

13
Frequency Shift Keying

• 0 1
• To find Pb

14
Minimizing Pb

• Minimize Epq to minimize Pb

15
FSK Probability of Bit Error
ASK

• Assuming
• Pr(1)Pr(0)
• EbEqEpA2Tb
• Epq - 0. 217A2Tb

BPSK
FSK
16
Minimum Shift Keying MSK

• IF
• THEN orthogonal signaling
• Smallest possible value is
• This separation avoids the abrupt phase changes
  at bit transition, continuous phase FSK (CP-FSK)
• Tradeoff is slightly higher Pb in exchange for
  faster spectrum roll-off and better power
  efficiency

17
MSK Spectrum

• BW is 1.5 Rb
• Spectrum decays as 1/f 4
• Orthogonal signaling,

18
MSK Performance

• Performance can be improved by looking over
  multiple bit intervals since the phase depends on
  past bit intervals
• Bandwidth is 1.5 Rb
• Spectrum decays as 1/f4 (helps minimize ISI)
• Related to OQPSK (will look at this next lecture)

19
Noncoherent Detection

• Phase is unknown
• Use filter and techniques such as envelope
  detection or feedback to demodulate signal

H(w)
Envelope Detector
Threshold detector
20
Amplitude Shift Keying

• Filter, H(w) is a BPF matched to RF pulse
• If a 1 sent, received signal after BPF is
• From section11.5 in text, the envelope of this
  signal has a Rician Density

21
Small Noise Case Apgtgtsn

• In this case, result is approximately Gaussian
• If a 0 sent, the envelope of the received
  signal is Rayleigh distributed

22
Optimum Threshold
prm

• Optimum threshold value occurs where densities
  intersect
• Threshold depends on bit SNR, problem in fading
  channels

r
Optimum Threshold
23
Pb Calculations

• Recall
• If signal probabilities equally likely

24
Compare with Coherent ASK

• For large signal case
• Noncoherent
• Coherent

Non coherent ASK
Coherent ASK
25
Noncoherent FSK

• Filters matched to RF pulses for 0 and 1
• Decide 0 if r0 gt r1
• Decide 1 if r1 gt r0

r1
Env. Det
Sampler
H1(w)
Comparator
Env. Det
Sampler
H0(w)
r0
26
Performance Assessment

• Outputs of the envelope detectors have Rician
  densities when signal is present, Rayleigh when
  only noise, in the case where 1 is sent

27
Analysis (II)

• This system decides m1 if r1gtr0 and m0 if r0gtr1
• Error occurs if r0gtr1 when 1 is sent.

28
Analysis (III)

29
Analysis (IV)

P(1)1/2
P(0)1/2
Similar to ASK, but with fixed threshold, and
larger bandwidth
30
Next Time

• Reading Lathi 13.5 M-ary Systems
• Review quiz 3
• Homework 5
• Project discussion